Question: Solve for $x$ and $y$ using elimination. ${4x-3y = -26}$ ${-3x+3y = 27}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {4x-3y = -26}\thinspace$ to find $y$ ${4}{(1)}{ - 3y = -26}$ $4-3y = -26$ $4{-4} - 3y = -26{-4}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {-3x+3y = 27}\thinspace$ and get the same answer for $y$ : ${-3}{(1)}{ + 3y = 27}$ ${y = 10}$